There are, with many more examples historically.
Konkani in the Devanagari script is an official language of India & the state language of Goa - while Christian Konkanis (a sizable proportion of the population) prefer to write it in the Latin script.
Kashmiri Pundits used the Sharda script, while Muslim Kashmiris wrote it in the Persian script.
Historically, the picture is more complicated. People were familiar with multiple scripts, and shifted across them based on context and jargon. For example, when the British took Sindh from the Nawab, they found the natives writing the same language in multiple scripts. The administration of the erswhile Nawab worked in Persian, while merchants used Khudabadi, a landa script related to Gurmukhi. They found that women in the home preferred the Devanagari script, as did the priestly class. Since the British were most concerned with the needs of the Persianate clerks, they mandated that Sindhi only in the Persian script would be taught in schools. You will find similar situations across India, with people adopting scripts geared towards the audience they were writing to, rather than an exclusive formalized script unique to a language. Literate Medieval Indian would be fluent in multiple languages and scripts, and combined them in interesting ways.
On a tangent, I recall an argument by Bhagat Singh that the different languages of India should adopt a common script to foster unity - Devanagari in his opinion.